Basic properties
| Modulus: | \(4024\) | |
| Conductor: | \(4024\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(502\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4024.m
\(\chi_{4024}(5,\cdot)\) \(\chi_{4024}(29,\cdot)\) \(\chi_{4024}(37,\cdot)\) \(\chi_{4024}(45,\cdot)\) \(\chi_{4024}(53,\cdot)\) \(\chi_{4024}(93,\cdot)\) \(\chi_{4024}(101,\cdot)\) \(\chi_{4024}(109,\cdot)\) \(\chi_{4024}(125,\cdot)\) \(\chi_{4024}(133,\cdot)\) \(\chi_{4024}(149,\cdot)\) \(\chi_{4024}(157,\cdot)\) \(\chi_{4024}(165,\cdot)\) \(\chi_{4024}(181,\cdot)\) \(\chi_{4024}(213,\cdot)\) \(\chi_{4024}(221,\cdot)\) \(\chi_{4024}(245,\cdot)\) \(\chi_{4024}(261,\cdot)\) \(\chi_{4024}(269,\cdot)\) \(\chi_{4024}(277,\cdot)\) \(\chi_{4024}(309,\cdot)\) \(\chi_{4024}(333,\cdot)\) \(\chi_{4024}(341,\cdot)\) \(\chi_{4024}(349,\cdot)\) \(\chi_{4024}(357,\cdot)\) \(\chi_{4024}(365,\cdot)\) \(\chi_{4024}(381,\cdot)\) \(\chi_{4024}(405,\cdot)\) \(\chi_{4024}(437,\cdot)\) \(\chi_{4024}(453,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{251})$ |
| Fixed field: | Number field defined by a degree 502 polynomial (not computed) |
Values on generators
\((1007,2013,2017)\) → \((1,-1,e\left(\frac{371}{502}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 4024 }(37, a) \) | \(-1\) | \(1\) | \(e\left(\frac{397}{502}\right)\) | \(e\left(\frac{60}{251}\right)\) | \(e\left(\frac{140}{251}\right)\) | \(e\left(\frac{146}{251}\right)\) | \(e\left(\frac{271}{502}\right)\) | \(e\left(\frac{71}{502}\right)\) | \(e\left(\frac{15}{502}\right)\) | \(e\left(\frac{121}{502}\right)\) | \(e\left(\frac{164}{251}\right)\) | \(e\left(\frac{175}{502}\right)\) |